School of Data and Computer Science, Sun Yat-Sen University, Guangzhou, 510006, Guangdong, China.
Department of Mathematics, National Cheng Kung University, 1 University Road, Tainan, 701, Taiwan.
Med Biol Eng Comput. 2020 Sep;58(9):2131-2141. doi: 10.1007/s11517-020-02220-x. Epub 2020 Jul 16.
The fast hybrid operator splitting (HOS) and stable uniformization (UNI) methods have been proposed to save computation cost and enhance stability for Markov chain model in cardiac cell simulations. Moreover, Chen-Chen-Luo's quadratic adaptive algorithm (CCL) combined with HOS or UNI was used to improve the tradeoff between speedup and stability, but without considering accuracy. To compromise among stability, acceleration, and accuracy, we propose a generalized Trotter operator splitting (GTOS) method combined with CCL independent of the asymptotic property of a particular ion-channel model. Due to the accuracy underestimation of the mixed root mean square error (MRMSE) method, threshold root mean square error (TRMSE) is proposed to evaluate computation accuracy. With the fixed time-step RK4 as a reference, the second-order GTOS combined with CCL (30.8-fold speedup) for the wild-type Markov chain model with nine states (WT-9 model) or (7.4-fold) for the wild-type Markov chain model with eight states (WT-8 model) is faster than UNI combined with CCL (15.6-fold) for WT-9 model or (1.2-fold) for WT-8 model, separately. Besides, the second-order GTOS combined with CCL has 3.81% TRMSE for WT-9 model or 4.32% TRMSE for WT-8 model more accurate than 72.43% TRMSE for WT-9 model or 136.17% TRMSE for WT-8 model of HOS combined with CCL. To compromise speedup and accuracy, low-order GTOS combined with CCL is suggested to have the advantages of high precision and low computation cost. For high-accuracy requirements, high-order GTOS combined with CCL is recommended. Graphical abstract.
快速混合算子分裂（HOS）和稳定均匀化（UNI）方法已被提出，以节省计算成本并增强心脏细胞模拟中马尔可夫链模型的稳定性。此外，Chen-Chen-Luo 的二次自适应算法（CCL）与 HOS 或 UNI 结合使用，以改善速度和稳定性之间的权衡，但不考虑准确性。为了在稳定性、加速和准确性之间进行折衷，我们提出了一种与特定离子通道模型的渐近特性无关的广义 Trotter 算子分裂（GTOS）方法，该方法与 CCL 相结合。由于混合均方根误差（MRMSE）方法的准确性低估，提出了阈值均方根误差（TRMSE）来评估计算准确性。以固定时间步长 RK4 作为参考，二阶 GTOS 与 CCL 相结合（WT-9 模型的速度提高 30.8 倍，WT-8 模型的速度提高 7.4 倍）比 UNI 与 CCL 相结合（WT-9 模型的速度提高 15.6 倍，WT-8 模型的速度提高 1.2 倍）更快。此外，二阶 GTOS 与 CCL 相结合的 WT-9 模型的 TRMSE 为 3.81%，WT-8 模型的 TRMSE 为 4.32%，比 HOS 与 CCL 相结合的 WT-9 模型的 72.43% TRMSE 或 WT-8 模型的 136.17% TRMSE 更准确。为了在速度和准确性之间进行折衷，建议使用低阶 GTOS 与 CCL 结合，以具有高精度和低计算成本的优势。对于高精度要求，建议使用高阶 GTOS 与 CCL 结合。
